Recent questions tagged medium

If $ \tan^{-1}a+\tan^{-1}b+\tan^{-1}c=\pi,\;prove\;that\;a+b+c=abc.$

asked Jan 24, 2013 by meena.p

1 answer

Solve for x $ \sin^{-1}\frac{2\alpha}{1+\alpha^2}+ \sin^{-1}\frac{2\beta}{1+\beta^2}=2\tan^{-1}x.$

asked Jan 24, 2013 by meena.p

1 answer

Prove that :$\cot^{-1}\bigg[\frac{ab+1}{a-b}\bigg]+\cot^{-1}\bigg[\frac{bc+1}{b-c}\bigg]+\cot^{-1}\bigg[\frac{ca+1}{c-a}\bigg]=0$

asked Jan 24, 2013 by meena.p

1 answer

In any Triangle ABC, if $ A=\tan^{-1}2\;and\;B=\tan^{-1}3,$prove that $C=\frac{\pi}{4}$

asked Jan 24, 2013 by meena.p

1 answer

Prove that $\sin2[\cot^{-1}\{\cos(\tan^{-1}x)\}]=2\frac{\sqrt{x^2+1}}{x^2+2}$

asked Jan 24, 2013 by meena.p

1 answer

If $ \cos^{-1}\frac{x}{a}+\cos^{-1}\frac{y}{b}=\alpha,$prove that $\frac{x^2}{a^2}-\frac{2xy}{ab}\cos \alpha+\frac{y^2}{b^2}=\sin^2\alpha.$

asked Jan 23, 2013 by meena.p

1 answer

Prove that $4\tan^{-1}\large\frac{1}{5}-\tan^{-1}\frac{1}{70}+\tan^{-1}\frac{1}{99}=\large\frac{\pi}{4}$

asked Jan 23, 2013 by meena.p

1 answer

Prove that $\cos\bigg\{2\cot^{-1}\sqrt{\large\frac{1-x}{1+x}}\bigg\}+x=0$

asked Jan 23, 2013 by meena.p

1 answer

If $x>0$ and $\sin^{-1}\bigg(\large{\frac{5}{x}}\bigg)+\sin^{-1}\bigg(\frac{12}{x}\bigg)=\large\frac{\pi}{2},$ than find the value of $x$.

asked Jan 23, 2013 by meena.p

1 answer

If $\cos^{-1}x=\tan^{-1}x,\;show\;that\;\sin(\cos^{-1}x)=x^2$

asked Jan 23, 2013 by meena.p

1 answer

Find the value of x if $cosec^{-1}x=2\cot^{-1}7+\cot^{-1}\frac{3}{4}$

asked Jan 23, 2013 by meena.p

1 answer

Simplify $\tan^{-1}\big(\large \frac{\cos x}{1+\sin x}\big)$

asked Jan 23, 2013 by meena.p

1 answer

Solve for x : \[ tan^{-1} \bigg( \frac{2x}{1-x^2} \bigg) +cot^{-1} \bigg( \frac{1-x^2}{2x} \bigg) = \frac{\pi}{3}, x > 0\]

asked Jan 23, 2013 by thanvigandhi_1

1 answer

True-or-False: Solution of $x\frac{dy}{dx} - y = x\tan\frac{y}{x}$ is $\sin\bigg(\frac{y}{x}\bigg)=kx$.

asked Jan 21, 2013 by sreemathi.v

1 answer

True-or-False: The solution of the differential equation $\large\frac{dy}{dx} = \frac{x+2y}{x}$ is $x+y=kx^2$.

asked Jan 21, 2013 by sreemathi.v

1 answer

True-or-False: Differential equation representing the family of curves $y=e^x(A\cos x+B\sin x)$ is $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 2y = 0$.

asked Jan 21, 2013 by sreemathi.v

1 answer

The solution of the differential equation $y dx + (x + xy) dy = 0$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

General solution of $\frac{dy}{dx} + y\tan x = \sec x$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

Which of the following is the general solution of $\large\frac{d^2y}{dx^2}$$-2\large\frac{dy}{dx}$$+y=0$

asked Jan 20, 2013 by sreemathi.v

1 answer

The differential equation of the family of curves $y^2=4a(x+a)$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of $\large\frac{dy}{dx}$$+y=e^{-x},y(0)=0$ is

asked Jan 20, 2013 by sreemathi.v

1 answer

The solution of the equation $(2y-1)dx-(2x+3)dy=0$ is\[(A)\;\frac{2x-1}{2y+3}=k \quad (B)\;\frac{2y+1}{2x-3}=k \quad (C)\;\frac{2x+3}{2y-1}=k \quad (D)\;\frac{2x-1}{2y+1}=k \]

asked Jan 20, 2013 by sreemathi.v

1 answer

The general solution of the differential equation $\large\frac{dy}{dx} $$=e^{\large\frac{x^2}{2}}+xy$ is :\[(A)\;y=ce^{\large\frac{x^2}{2}} \quad (B)\;y=-ce^{\large\frac{x^2}{2}} \quad (C)\;y=(x+c)e^{\large\frac{x^2}{2}} \quad (D)\;y=(c-x)e^{\large\frac{x^2}{2}}\]

asked Jan 19, 2013 by sreemathi.v

1 answer

The differential equation of the family of curves $x^2+y^2-2ay=0$,where a is arbitrary constant,is\[(A)\;(x^2-y^2)\frac{dy}{dx}=2xy \quad (B)\;2(x^2+y^2)\frac{dy}{dx}=xy \quad (C)\;2(x^2-y^2)\frac{dy}{dx}=xy \quad (D)\;2(x^2+y^2)\frac{dy}{dx}=2xy\]

asked Jan 19, 2013 by sreemathi.v

1 answer